Analytical estimation of performance of a sensor system

ABSTRACT

The invention relates to a method for an analysis tool for analysisis of the sensor performance of a system of sensors, which method comprises analytical calculation of a sensor system&#39;s measurement characteristics at each point in a given geographical area. The method comprises obtaining performacne parameters ( 1, 2, 3 ) from N sensors that are in the system. The method is characterized in that a set of analytical performance parameters ( 5 ) for the system is calculated by the performance parameters ( 1, 2, 3 ) being fused irrespective of the different measurement characteristics of the sensors in the system with regard to the given perforamance parameters ( 1, 2, 3 ) and in that the analyticcal parameters are used in the analysis of the performance of the sensor system. The invention also relates to a device for use of the method and to the use of the method and the device.

TECHNICAL FIELD

[0001] Method for an analysis tool for analysis of the sensorperformance of a system of sensors, which method comprises analyticalcalculation of a sensor system's measurement characteristics at eachpoint in a given geographical area. The method comprises obtainingperformance parameters from Ns sensors that are in the system. Theinvention also relates to a device for use of the method and to the useof the method and the device.

BACKGROUND ART

[0002] A sensor is a device that receives signals of various types, forexample electromagnetic signals such as heat or radio signals, orsignals such as sound waves. There are passive sensors that only receivesignals, and active sensors that send out a signal that is reflectedagainst an object and thereafter returns to the sensor where the signalis read off. An active sensor can calculate distance and bearing of anobject, for example by measuring the time it takes for a pulse signal toreturn and by using a directional antenna. The passive or active sensorhas predetermined specific characteristics.

[0003] A further type of sensor is an adaptive sensor, which can becaused to change its characteristics depending upon how an objectbehaves, for example to increase the sweep frequency or the intensity,over a particular area within the range of the sensor.

[0004] A radar is a typical sensor as above, intended to detect targetsand track targets using electromagnetic waves. The following descriptionof the background art refers principally to radar, but as other sensorscan also be used, the term sensor is used instead of radar.

[0005] A sensor's measurement characteristics are often described as anumber of performance parameters:

[0006] p_(fa)=the probability of false alarms per scan in a particularpartial area,

[0007] p_(ss)=detection probability per scan (the subscript ss refers tosingle scan) for targets with a particular target area,

[0008] R=measurement accuracy, here expressed as a covariance matrix,and

[0009] T=detection time for the sensors search area.

[0010] From these parameters the sensor's average measurement rate (oreffective measurement rate), $\frac{1}{T_{e}},$

[0011] can be calculated as $\frac{1}{T_{e}} = \frac{p_{s\quad s}}{T}$

[0012] The first three parameters, p_(fa), p_(ss) and R, often varyacross the sensor's search area. The detection ability of the sensorcan, for example, be given a value by calculating the distance from thesensor where the probability of detection is 0.5. This distance is oftencalled R_(50ss). By means of this value, the sensor's detectioncharacteristics can be shown graphically by means of geometric figuresin the form of circles or parts of circles where the value R_(50ss) isscaled in such a way that the scaled value of R_(50ss) constitutes theradius of the said figures, preferably together with a map of the areain question. The area that is described by the geometric figures isoften called the sensor's range.

[0013] Certain existing planning tools (analysis tools) for sensors arebased on ranges of the type described above and, in addition, cansometimes take into account topography and calculate restrictions in therange due to topographical masks by means of access to a map database.

[0014] A sensor's tracking characteristics can be described in acorresponding way as for the said detection characteristics, with arange R_(50ss) given that a target approaches the sensor radially at aparticular speed. This is described in Reference 1.

[0015] Problems arise when the performance of a system of sensors is tobe calculated. The difficulty consists of obtaining an idea of thesystem's characteristics, in particular with respect to the tracking,when the sensors have greatly varying characteristics, not only withregard to the ranges but also with regard to other characteristics suchas measurement rate, measurement accuracy and false alarms.

[0016] For tracking of targets measured by a plurality of sensors, thefiltering of target data is already known. The two most commontechniques are:

[0017] 1. The sensors track the target separately and the result isthereafter fused.

[0018] 2. The measurements are fused and a tracking filter is thereafterused on the resulting measurement.

[0019] These methods relate to fusion of data in real systems, but canin principle also be applied for certain analysis analysis.

[0020] The filtering of target data according to point 1 comprises thecalculation of a tracking filter, often a Kalman filter, for eachsensor. For fusion of these values, the values in the filter'scovariance matrix are to be fused, which involves laborious calculationsthat require a lot of data capacity and take a long time. A furtherproblem is that in fusion of tracking data, the degree of correlationbetween the estimates is not known, which is not possible to calculatein real systems. In an analysis it should, however, be possible tocalculate the correlations, but these calculations would add to thealready laborious calculations.

[0021] In filtering target data according to point 2, a plurality ofvariants can arise, two of which variants (2a and 2b) will beillustrated in greater detail below. This is also described in Reference3.

[0022] For fusion according to 2a, the fusion consists in the actualcase of the measurement data being processed in the chronological orderin which they are received, that is the contributions from the differentsensors are received at different times and are processed by a commonfilter. This is, however, not applicable in the analytical case in whichan evaluation of a system's performance is to be carried out. Actualmeasurement values are then not available, but only the generalcharacteristics of the measurement values as described above. A fusionof these characteristics is to be carried out, but there are problemsrelating to randomness.

[0023] For fusion according to 2b, the measurements are fused beforethey are passed through a tracking filter. This can be carried out intwo ways (2b1 and 2b2). In order to be able to utilise a filteraccording to 2b1, simultaneity is required for the measurements that arebeing fused. By simultaneity is meant here that the measurements arecarried out at the same moment for all the sensors in the system andthat there are no deviations in the measurement rate, detectioncharacteristics or angle or distance to the measurement object. For useof a filter according to point 2b2 above, the measurements for thedifferent sensors are weighted, fused, using known mathematical methodsin which the accuracy of the weighted values, that is the variance, iscalculated according to the equation (7-1) below. $\begin{matrix}{R_{j} = \{ {\sum\limits_{i = 1}^{N_{S}}\quad R_{i}^{- 1}} \}^{- 1}} & ( {7\text{-}1} )\end{matrix}$

[0024] This equation applies, however, only if the simultaneitydescribed above is fulfilled, which in practice means that there are nodeviations in measurement rate, detection characteristics or angle ordistance to the measurement object. The probability of these criteriabeing fulfilled for a system of sensors that are tracking a mobilemeasurement object is very small, almost non-existent.

[0025] For fusion according to 2b2, the measurement vector is increased,instead of the measurement values being weighted and combined. In thiscase, the measurement contributions of the different sensors are addedto a vector in sequence, with the result that a large measurement matrixis obtained which gives intensive calculations for calculating thetracking filter. In order to illustrate the problem, it can be mentionedthat a measurement vector with n elements gives rise to a covariancematrix of n² elements. Simultaneity is also required in the 2b2 case,with the problems mentioned above in the discussion concerning 2b1.

[0026] Some further disadvantages of existing technology are that onlyan idea of the measurement characteristics of the sensor(s) is obtainedin the form of range and measurement accuracy. This is often combinedwith map databases in order to give an idea of the range of the sensorsystem, in the form of topographical masks and the like. These methodsdo not give performance for the sensor system as a whole, for example inthe form of which tracking characteristics these measurementcharacteristics can be expected to provide.

[0027] There is a requirement to be able to carry out an analysis ofsensor performance for a system of sensors, for planning the positioningof sensors in a particular area to be monitored. Sensor performance isnormally calculated and described during design and purchasing. There isin addition an increasing need:

[0028] to evaluate necessary sensor resources (or alternatively, howexisting resources are best to be utilised), in planning an assignmentin which sensors are to be used,

[0029] to match the sensor resources to the situation in question inreal time; so called reactive searching,

[0030] to evaluate the effect of possible or proposed measures/changesfor adaptive sensors, both as automatic and manual “decision supports”.

[0031] Further disadvantages of previously known technology are that therequirements that are described above cannot be fulfilled by previouslyknown analysis methods.

DISCLOSURE OF INVENTION

[0032] The invention aims to solve the problems/disadvantages that aredescribed above and aims to provide an analysis tool for analysis ofsensor performance in a system of sensors. The invention thus solvesamong other things the problem of “calculating analytically” thesystem's performance parameters, analytical performance parameters, thatcan provide measurement characteristics and tracking performance at eachpoint in a given geographical area for a system of sensors, that is whenseveral sensors “measure” the same target. A typical sensor in a sensorsystem of the abovementioned type is a radar, but the use of the methodaccording to the invention for calculating analytical performanceparameters for a sensor system can also be used for other types ofsensor. The term sensor will therefore be used in the following insteadof the term radar.

[0033] By “calculating analytically” is meant calculating expectedperformance using mathematical methods on the basis of knowncharacteristics of the sensors and the measurement objects, in contrastto calculating the performance of a real system in a situation whereactual measurements are carried out. In cases where there are randomphenomena, firstly effective values for characteristics/performance andsecondly spread measurements for variations around the effective valuesare calculated analytically. The effective value is calculated usingformulae which are presented in the following text, where the subscript“e” stands for the effective parameter.

[0034] The problem of sensor systems according to previously knowntechnology consists partly of the fact that the sensors can have varyingmeasurement characteristics, and partly of calculating trackingperformance not only for a given target path, but also calculatingperformance over the surface (volume) that the sensor system is tomonitor.

[0035] The invention thus consists of a method for an analysis tool foranalysis of sensor performance for a system of sensors, which methodcomprises analytical calculation of a sensor system's measurementcharacteristics at each point (for the purposes of calculation, however,a raster of points is selected in practice) in a given geographicalarea. The method comprises obtaining performance parameters from N_(s)sensors that are in the system. The method according to the invention ischaracterized in that:

[0036] a set of analytical performance parameters for the system iscalculated by the performance parameters being fused irrespective of thedifferent measurement characteristics of the sensors in the system withregard to the given performance parameters and in that:

[0037] the analytical parameters are used in the analysis of theperformance of the sensor system.

[0038] Obtaining performance parameters comprises obtaining performanceparameters comprising:

[0039] p_(ss,i)=detection probability per scan (the subscript ss refersto single scan) at a particular point for targets with a particulartarget area for the sensor N_(s)=i;

[0040] R_(i)=measurement accuracy expressed as a covariance matrix forthe sensor N_(s)=i;

[0041] T_(i)=detection time for the search area of the sensor N_(s)=i,and

[0042] p_(fa,i)=the probability of false alarms for a sensor N_(s)=i.

[0043] The calculation of the analytical performance parameterscomprises calculations based on selected performance parameters, whichcalculations comprise the formulae: $\begin{matrix}{{T_{j} = ( {\sum\limits_{i = 1}^{N_{S}}\quad T_{i}^{- 1}} )^{- 1}}\quad} & ( {7\text{-}2} ) \\{{\frac{1}{T_{e\quad j}} = {\sum\limits_{i = 1}^{N_{S}}\frac{p_{{s\quad s},i}}{T_{i}}}}\quad} & ( {7\text{-}3} ) \\{{{p_{{s\quad s},j} = \frac{T_{j}}{T_{e\quad j}}},}\quad} & ( {7\text{-}4} ) \\{{\frac{1}{T_{e\quad i}} = \frac{p_{{s\quad s},i}}{T_{i}}}\quad} & ( {7\text{-}5} ) \\{\quad {\mu_{i} = \frac{T_{e\quad j}}{T_{e\quad i}}}\quad} & ( {7\text{-}6} ) \\{\quad {R_{j} = \{ {\sum\limits_{i = 1}^{N_{S}}{\mu_{i}R_{i}^{- 1}}} \}^{- 1}}\quad} & ( {7\text{-}7} ) \\{\quad {p_{{f\quad a},j} = {\{ {\sum\limits_{i = 1}^{N_{s}}\frac{p_{{f\quad a},i}}{T_{i}}} \} T_{j}}}} & ( {7\text{-}8} )\end{matrix}$

[0044] where $T_{j},\frac{1}{T_{e\quad j}},$

[0045] p_(ss,j), μ_(i), R_(j) and p_(fa,j) are the analyticalperformance parameters, where N_(s) stands for the number of sensors inthe system and where the subscript j stands for “joint”, that isresulting.

[0046] The measurement error covariances. are described here in a commonCartesian coordinate system. The resulting first covariance matrix,R_(j), for measurement errors for the sensor system is calculated usinga method that differs from known methods, with the difference thataccording to the invention the contribution of the individual sensors isto be weighted by μ_(i), see equation (7-6).

[0047] The analytical parameter μ_(i) refers to a weighting measurementfor the contribution to the system of each sensor in the system,consisting of the effective measurement rate,$\frac{1}{T_{e\quad i}},$

[0048] for the sensor N_(s)=i, being divided by the analytical parameter“effective measurement rate for the system”, $\frac{1}{T_{e\quad j}}.$

[0049] The weighting by μ_(i) means that the calculations of theanalytical performance parameters for the system are independent of theactual variations in the measurement processes of the sensors in thesystem, for example p_(ss,i) which is the detection probability per scanfor targets with a particular target area for the sensor N_(s)=i, themeasurement rate $\frac{1}{T_{i}}$

[0050] or the actual geometric relationship of the measurement object tothe respective sensor. This means that the invention has solved theproblem of analytically calculating performance for a system of sensorswith different measurement characteristics with regard to the givenperformance parameters. The sensor system can thus be regarded as onesensor for specified analytical purposes.

[0051] In the description of previously known technology, it wasmentioned that fusion of the measurements according to 2b and equation(7-1) are applicable provided that the conditions for simultaneity arefulfilled, which is itself unrealistic, for which reason such methodsare not applicable for calculating the performance of the sensor systemaccording to the invention. According to the above, μ_(i) is used in theequation (7-7) in order to weight the contribution of the sensors andmake possible fusion and calculation of the performance of a sensorsystem. When there is simultaneity, in certain cases, μ_(i)=1 and theequation (7-1) will be applicable, however it should be added that theequation (7-1) can only be used when there are no deviations between thesensors in measurement rate, detection characteristics or angle ordistance to the measurement object. The only way to achieve this in thecase of a target that is in the vicinity of the sensors is to put thesensors at the same point with the same performance, which in principleinvolves the use of one sensor.

[0052] According to the invention, irrespective of the position orperformance of the sensors it is possible to combine the sensors'measurement values by each sensor's detection time, T_(i), being dividedup into N_(s) equal time components which spread the measurementsequally, which means that the measurement values are combined at thecommon created moments of time for the time components. In this way, anaverage is obtained for the behaviour of each sensor, with an increasein the variance of N_(s) in size as a result. By means of the saidmethod, the problem of simultaneity and synchronisation is avoided.

[0053] The measurement characteristics of the sensor system areestimated by reading off all the analytical performance parameterscalculated for the system, $T_{j},\frac{1}{T_{e\quad j}},$

[0054] p_(ss,j), μ_(i), R_(j) and p_(fa,j). It can be mentioned thatthrough its different elements in the matrix, the covariance matrix,R_(j), corresponds to the measurement error in, for example, theposition of a target or measurement object, in relation to a selectedsystem. Such a selected system is preferably a Cartesian coordinatesystem, but can also be another system that is suitable for the purpose.

[0055] The analytical parameter p_(ss,j)=detection probability per scanfor targets with a particular target area at a particular point in thesensor system.

[0056] The invention also consists of a method for calculating trackingperformance for the sensor system, both for given target paths and alsogenerally over the whole given area. The calculation described above ofthe tracking performance for a sensor is already known, but it has notpreviously been possible to calculate the tracking performance for asystem of sensors analytically, unless the simultaneity condition wasfulfilled. The invention can be used to calculate either the system's“stationary” characteristics or the system's “dynamic” characteristicsusing the said formulae.

[0057] By the system's “stationary” characteristics is meant that afilter's stationary state is calculated at each point over the area,that is identical measurements are carried out over a period of timeuntil a fictitious stationary state, a quasi-stationary state, isattained at the point in question.

[0058] By the system's “dynamic” characteristics is meant the system'scharacteristics given particular target speed and target course.According to the invention, the system's dynamic characteristics areobtained by parallel target paths being generated over the area and afilter being applied to these target paths. The said filter can bedimensioned according to various forecasts concerning the manoeuvringcharacteristics of the target in order to illustrate the system'sability to track under the prevailing conditions. A suitable filter forthe invention is a Kalman filter, but there can be other filters thatare suitable for the invention.

[0059] The said formulae are used for calculating the measurementcharacteristics of the sensor system and the analytical performanceparameters are used for calculating tracking performance for the sensorsystem in order to calculate with a filter the sensor system's trackingperformance for tracking measured objects. The filter for the systemgives a second covariant matrix, P, which is read off as a covariancematrix that indicates the sensor system's tracking accuracy at eachpoint in a given area. The elements in the said second covariancematrix, P, refer to variances, for example variances of positions,speeds and accelerations.

[0060] Based on the results that are obtained by means of the trackingperformance described above, a number of characteristics for the systemcan now be described, such as, for example, tracking accuracy, risks ofconflict with other targets or false alarms, the number of targets thatcan be tracked, etc.

[0061] A great advantage of the method according to the invention ofanalytically calculating tracking performance for a sensor systemaccording to the above, is that the sensor system's measurementcharacteristics are defined at each point in the space. The trackingcharacteristics for the system can thereby be calculated by using onlyone tracking filter for the sensor system, which differs from previouslyknown technology in which a filter for each sensor is used. As themeasurement characteristics of the sensors are ideally stored together(all the measurements are used) an idea is also obtained in this way ofthe possible performance of the sensor system.

[0062] By means of the description of the sensor system's measurementcharacteristics as above, it is possible to calculate probabilities forvarious events that affect the tracking procedure by the utilisation ofa calculated measurement rate, $\frac{1}{T_{j}},$

[0063] the detection probability, p_(ss,j) and the probability of falsealarms p_(fa,j), for the sensor system together with Markov analysis.The calculated measurement rate, $\frac{1}{T_{j}},$

[0064] consists of the reciprocal value of the analytical parameter,T_(j), which refers to the searching time for the search area of thesensor system at a particular given point. This method can be used todetermine the detection range, that is where along a particular targetpath the target is detected for the first time. When tracking a target,it is also important to know the detection criterion in order to knowwhen tracking is to commence. The detection criterion gives anacceptable level for the number of detections per number of attempts todetect a target. In this connection, it is also interesting to know thecapturing range, that is where in the target path the capturingcriterion is fulfilled, and corresponding termination criteria, that iswhere and when the tracking is terminated. All these cases can beevaluated analytically on the basis of the method according to theinvention, utilising the measurement rate for the system, the detectionprobability and the probability of false alarms for the system togetherwith Markov analysis, according to the above.

[0065] As mentioned above, it is also possible according to theinvention to utilise the sensor system's measurement characteristics incalculating a filter for the tracking characteristics of the sensorsystem. For calculating a filter for tracking characteristics, thecalculated effective measurement rate, $\frac{1}{T_{j\quad e}},$

[0066] for the system is utilised, which effective measurement rate is aform of averaging of the measurement rates of the sensors in the systemaccording to the formula (7-3). The detection probability, p_(j,ss),then becomes equal to 1 for the system. The effective measurement rateis used to eliminate random errors in the system, that is differences inmeasurement rate, detection characteristics (detection probability, etc)or angle or distance to the measurement object.

[0067] The tracking characteristics are then calculated on the basis ofthese measurement characteristics for the system of sensors. This can becarried out according to the invention both for given target paths andalso for describing characteristics within a particular area (orvolume).

[0068] The tracking performance of the sensor system can be calculatedfor a given target path. The covariance matrix for the prediction error(error in forecast) of a filter, for example a Kalman filter, can alsobe used to evaluate the risk of tracking being confused with falsealarms or other targets. In order to describe the sensor system'stracking characteristics in an area, the following steps are carried outaccording to the invention:

[0069] 1. According to the invention a user can either choose tocalculate tracking characteristics for a particular target pathdirection or to calculate the tracking characteristics using thepreviously described quasi-stationary state. For certain target paths,targets are generated on straight paths, at particular intervals, from aselected direction. For these target paths, the tracking characteristicsare calculated that are intended to be illustrated. Methods for carryingthis out can be read in Reference 1. Certain tracking characteristicsare dependent upon the direction of the target path in relation to themeasuring sensors.

[0070] 2. Dependent upon the requirements and/or the application, thetracking characteristics can now be selected to be represented bythree-dimensional graphs (where the height coordinate represents thevalue of the characteristic) of the selected area, with “level curves”marking the areas where the characteristics fulfil certain conditions orwith a single numeric value by the characteristics being integrated overthe selected area.

[0071] For adaptive sensors, the measurement rate is not known inadvance, but depends upon the number of targets and upon how thesensor's time is divided between different tasks, for example thesensor's search frequency can be changed. According to the invention, asystem of such sensors, or system of sensors in which such sensors areincluded, can be analysed/described as follows:

[0072] 1. Measurements of the search function and tracking function aredefined as separate “sensors”, as above, and they are combined accordingto the technique described above according to the invention. As anexample, it can be mentioned that more sensor resources can be appliedto already established targets, which in itself involves control of thesensor's resources depending upon requirement.

[0073] 2. In addition, each adaptive sensor is described by a functionfor determining how the sensor's resources are to be used and forensuring that the two “sensor models” according to point 1) areconnected in the sense that they share the sensor's resources.

[0074] 3. A sensor system's combined adaptive capabilities can beanalysed by the system's measurement characteristics being determined inthe way that was described above. In the same way as for a singleadaptive sensor, the effects of a selected distribution between thesensor system's searching and tracking “tasks” can now be shown. Inaddition, it can, according to the invention, hereby be shown how theresources can be divided between the sensors in a suitable way. This ismade possible by the invention making possible a simple calculation ofthe characteristics of the whole sensor system, which is what is to beoptimised.

[0075] 4. The invention is particularly suitable for showing theperformance of an adaptive sensor system, given that certain targetpaths are generated.

[0076] The invention can also be used for showing the effects of alltargets in an area being given a particular tracking quality, given thata particular target density is specified.

[0077] For so-called passive sensors, where the target's distance cannotbe measured, the procedure is carried out in a corresponding way to thatdescribed above. For calculating the performance for given target paths,the known position of the target is used. For calculating the generalcharacteristics of the sensor system, the measurement characteristicsare determined, as described above, at a number of points in the area.The difference from the case with the active sensor is that inunfavourable geometries the description of measurement errors by acovariance matrix as above is not sufficient. The invention is therebywell suited for use of techniques described in Reference 2, with, forexample, multiple Kalman filters or extended Kalman filters.

[0078] As an example of the advantages of the invention, it can bementioned that a management centre can continually make forecasts of asensor system's performance and respond to queries such as, for example,“What happens to the system's performance if we move a sensor from oneposition to another?” or “Which sensor resources are required at aparticular position within the range of the system in order for thesystem to have a sufficiently high capacity at the given location?”.

[0079] Another example of how the invention can be used is when thereare mobile sensors in the system, which, on account of their mobility,affect the performance of the system depending upon their position inrelation to other sensors. In this case, the invention can respond towhether the mobile sensor can be allowed to move in the required way, orwhether the mobile sensor needs to be redirected in order to strengthenthe sensor system's characteristics at a particular point or in aparticular geographical area.

[0080] Reference 1: Kronhamn T. R., “Surveillance Performance”, Radar'95, IEEE International Radar Conference, 1995, Washington, USA.

[0081] Reference 2: Kronhamn T. R., “Target Range Estimation withCooperating Airborne Passive Sensors”, Radar '97, IEEE InternationalRadar Conference, Edinburgh, UK, 1997.

[0082] Reference 3: Gan Q., Harris J. C., “Comparison of Two MeasurementFusion Methods for Kalman-filter Based Multisensor Data Fusion”, IEEETrans. on AES, Vol. 37, No. 1, pp 273-280, January 2001.

DESCRIPTION OF DRAWINGS

[0083] The invention will be described below in greater detail, usingexamples of embodiments and with reference to the attached drawings, inwhich:

[0084]FIG. 1 shows a flow chart of a method according to an embodimentof the invention.

[0085]FIG. 2 shows a device for the use of a method according to theinvention.

[0086]FIG. 3 shows a sketch of range and target path according topreviously known technology for an exemplary sensor system comprisingthree sensors, i=1,2,3, with different measurement rates.

[0087]FIG. 4 shows a diagram of effective searching times, T_(ei), forthree individual sensors according to FIG. 3, and effective searchingtimes, T_(ej), according to the invention for the sensor system atdifferent times for a target defined in the sensor area.

ALTERNATIVE EMBODIMENTS

[0088]FIG. 1 shows a flow chart for a method according to an embodimentof the invention. The method is intended to be used with an analysistool for analysis of sensor performance for a system of sensors. Themethod is preferably intended to be used for radar, but can also be usedfor other types of sensor, for which reason the more general term“sensor” has been selected in the following text. The method comprisesanalytical calculation of a sensor system's measurement characteristicsat each point in a given geographical area, which method comprises:

[0089] obtaining performance parameters 1, 2, 3 from N_(s) sensors thatare in the system. In order to facilitate the description of theinvention, FIG. 1 shows performance parameters 1, 2, 3 being obtainedfrom three sensors 11, 12, 13 that are in the system, but the system is,of course, not limited to this number of sensors. The method ischaracterized in that:

[0090] a set of analytical performance parameters 5 for the system iscalculated 6 by the performance parameters 1, 2, 3, being fused 7irrespective of the different measurement characteristics of the sensorsin the system with regard to the given performance parameters and inthat:

[0091] the analytical parameters are used for analysis 8 of the sensorsystem's performance.

[0092] The result from the analysis 8 is presented 9 to a user in asuitable way, for example via a display or a printout. The analysisdepends, in addition, on which type of analysis the user requires. Acouple of different analyses will be discussed in greater detail below.

[0093] By “being fused” is meant the combining of the performanceparameters 1, 2, 3, of the respective sensors by means of calculations.

[0094] The performance parameters 1, 2, 3, each comprise:

[0095] p_(ss,i)=detection probability per scan for targets with aparticular target area for the sensor N_(s)=i;

[0096] R_(i)=measurement accuracy expressed as covariance matrix for thesensor N_(s)=i;

[0097] T_(i)=searching time for the search area for the sensor N_(s)=i,and:

[0098] p_(fa,i)=the probability of false alarms for a sensor.

[0099] The calculation of the analytical performance parameters 5comprises calculations on the basis of the performance parameters 1, 2,3, which calculations fuse the performance parameters 1, 2, 3, by use ofthe formulae: $\begin{matrix}{T_{j} = ( {\sum\limits_{i = 1}^{N_{S}}\quad T_{i}^{- 1}} )^{- 1}} & ( {7\text{-}2} ) \\{{\frac{1}{T_{e\quad j}} = {\sum\limits_{i = 1}^{N_{S}}\frac{p_{{s\quad s},i}}{T_{i}}}}\quad} & ( {7\text{-}3} ) \\{{{p_{{s\quad s},j} = \frac{T_{j}}{T_{e\quad j}}},}\quad} & ( {7\text{-}4} ) \\{{\frac{1}{T_{e\quad i}} = \frac{p_{{s\quad s},i}}{T_{i}}}\quad} & ( {7\text{-}5} ) \\{\quad {\mu_{i} = \frac{T_{e\quad j}}{T_{e\quad i}}}\quad} & ( {7\text{-}6} ) \\{\quad {R_{j} = \{ {\sum\limits_{i = 1}^{N_{S}}{\mu_{i}R_{i}^{- 1}}} \}^{- 1}}\quad} & ( {7\text{-}7} ) \\{\quad {p_{{f\quad a},j} = {\{ {\sum\limits_{i = 1}^{N_{s}}\frac{p_{{f\quad a},i}}{T_{i}}} \} T_{j}}}} & ( {7\text{-}8} )\end{matrix}$

[0100] where $T_{j},\frac{1}{T_{e\quad j}},$

[0101] p_(ss,j), μ_(i), R_(j) and p_(fa,j) comprise the analyticalperformance parameters, where N_(s) stands for the number of sensors inthe system (here N_(s)=3) and where the subscript j stands for “joint”,that is resulting.

[0102] The analytical parameters can be used for analysis ofprobabilities for different events that concern the tracking procedureand are calculated by using a calculated measurement rate,$\frac{1}{T_{j}},$

[0103] the detection probability, p_(ss,j) and the probability of falsealarms, p_(fa,j), for the sensor system together with Markov analysis.

[0104] The analytical parameters can be used for analysis of thesystem's tracking characteristics by a filter for the sensor systembeing calculated by using the calculated effective measurement rate,$\frac{1}{T_{e\quad j}},$

[0105] for the system.

[0106] The said formulae are used to calculate the sensor system'smeasurement characteristics in order to calculate with a filter thesensor system's tracking performance for tracking measured objects, andin order that

[0107] the filter for the system gives a covariant matrix, P, which isread off as a covariance matrix that gives the tracking accuracy of thesensor system at. each point in a given area.

[0108] Further analysis of the sensor system can be carried out by thesensor system's stationary characteristics being calculated by afilter's stationary state being calculated at each point over a givenarea, which calculation comprises the said formulae.

[0109] Further analysis of the sensor system can be carried out by thesensor system's dynamic characteristics being calculated by a filterbeing calculated based on parallel target paths of a target with givenvalues of speed and course, which calculation also comprises the saidformulae.

[0110] An additional advantage of the method according to the inventionusing fusion. of performance parameters as above for calculatinganalytical performance parameters for a system is obtained with adaptivesensors, each of which can be regarded as a sensor system. An adaptivesensor can thus be regarded as several different sensors, depending uponhow the adaptive sensor is adjusted.

[0111] The method for an analysis tool according to the above is usedpreferably by a device for analytical calculation of the sensor system'sperformance. Such a device can be, for example, a computer, which isalso used to display the sensor system's performance graphically to auser of the analysis tool with regard to required information, forexample the system's detection and tracking probabilities.

[0112]FIG. 2 shows a device 20 for use of a method according to anembodiment of the invention, where the sensor system comprises threesensors, 21, 22, 23, and the device comprises means 24 for combiningperformance parameters in the form of measurement characteristics fromthe respective said sensors 21, 22, 23. In order for the performanceparameters to be able to be transmitted from the respective sensor tothe device 20, a means 25 is used that is suitable for the purpose, forexample an interface, that is a device that converts signals, forexample from analog to digital, in order to make possible digital dataprocessing. The means 25 can also consist of a device that is used as asummation point of digital signals.

[0113] All the means mentioned in the text refer to devices suitable forthe purpose, for example an additional computer unit, an interface or asuitable algorithm in an existing computer.

[0114] The device also comprises means 26 for fusion of the performanceparameters by weighting the measurement contributions of the respectivesaid sensors 21, 22, 23, which device comprises means 27 for calculatinganalytical performance parameters for the sensor system, which means 27for calculating analytical performance parameters for the system isindependent of the different measurement values of the sensors in thesystem, for example random variations and different measurement rates,on account of the weighting of the respective said sensors' measurementcontribution. The means 27 for calculating analytical performanceparameters for the sensor system comprises, among other things, means 28for calculating a covariance matrix.

[0115] The device comprises means 29 for calculating a filter'sstationary state at each point over a given area.

[0116] The device comprises means 30 for calculating a filter's dynamiccharacteristics on the basis of parallel target paths for a target withgiven values of speed and course.

[0117] The device also comprises means 31 for presentation of analysisresults to a user. Such a means 31 can, for example, be a display or aprinter.

[0118] According to an embodiment of the invention, at least one of thesensors in the sensor system is a passive sensor.

[0119] According to a second embodiment of the invention, at least oneof the sensors in the sensor system is an active sensor.

[0120] According to yet another embodiment of the invention, at leastone of the sensors in the sensor system is an adaptive sensor.

[0121] According to yet another embodiment of the invention, at leastone of the sensors in the sensor system is a radar unit.

[0122] In order to illustrate further the advantages of the presentinvention, an example will be given below of how the analysis toolincreases a user's ability to analyse the system's performance. Theexample concerns the analysis of a target path and is illustrated withreference to FIGS. 3 and 4.

[0123]FIG. 3 shows a sketch of the range and target path according topreviously known technology for a sensor system comprising threesensors, i=1,2,3, with different measurement rates. In this case, thesensors concern three radar units that sweep 360 degrees, that is acomplete revolution per sweep, which means that the searching time,T_(i), for the search area of the sensor N=1 concerns a completerevolution. Another way of indicating how a radar sweeps is to specifythe measurement rate, which means the reciprocal value of the timebetween the measurements, that is $\frac{1}{T_{i}}.$

[0124]FIG. 3 shows a coordinate system for an area of X km (the x-axisin the sketch) and Y km (the y-axis in the sketch). The figure shows afirst sensor 31, a second sensor 32 and a third sensor 33. The origin inthe coordinate system has been placed in the centre of the second sensor32. The figure also shows the probabilities for detection of a targetwith one measurement (one sweep) by circles 311, 321, 331 having beendrawn for the sensors 31, 32, 33 respectively, marking the border of a50% probability of detecting the target with one measurement, that isthe circles show R_(50ss). The first sensor 31 has a searching timeT₁=5s, the second sensor 32 has a searching time T₂=1s and the thirdsensor 33 has a searching time T₃=2s.

[0125]FIG. 3 also shows a target path 34 for a target with a particulartarget area and with a constant speed of 250 m/s. The target pathconsists of a continuous line consisting of three straight paths withthree target manoeuvres in between. The first target manoeuvre 341 iscarried out between the times t=110s and t=120s at 3 g and the secondmanoeuvre 342 is carried out between the times t=260s and t=280s at 1 g.

[0126]FIG. 3 shows principally how a sensor system's performance isevaluated using previously known technology, in which the differentcircles 311, 321, 331 that indicate R_(50ss) have been drawn and aninterpretation of the range is carried out on the basis of thegeographical extent of the circles.

[0127]FIG. 4 shows a diagram of effective searching times, T_(e1), 411,T_(e2), 421, T_(e3), 431, for the three individual sensors 31, 32, 33respectively according to FIG. 3, and for the sensor system's effectivesearching times, T_(ej), 441, at different times for a target defined inthe sensor area. The effective searching times, T_(ei), are calculatedas $\frac{T_{i}}{p_{{s\quad s},i}}.$

[0128] The searching time T_(e)[s] is shown on the y-axis and the targetpath's time t [s] is shown on the x-axis. FIG. 4 also shows threeparallel broken lines 412, 422, 432 that indicate the respectiveeffective searching times, T_(e1), 411, T_(e2), 421, T_(e3), 431, whenthe detection probability for each sensor, p_(ss,i) is equal to one,that is the broken parallel lines 412, 422, 432 indicate the searchingtime of the respective sensor.

[0129]FIG. 4 shows clearly how the individual sensors' effectivesearching times, T_(e1), 411, T_(e2), 421 and T_(e3), 431 differ fromthe sensor system's effective searching times, T_(ej), 441. As theeffective searching time is dependent upon the reciprocal value of thedetection probability, the diagram is to be interpreted as showing thata high value on the y-axis means a low detection probability. Thedetection probability diminishes with the distance from the centre ofthe sensor, which can be seen, for example, at t=280 (the second targetmanoeuvre 342 in FIG. 3) where the first sensor's 31 effective searchingtime, T_(e1), 411 lies close to the parallel line 412, which marks adetection probability close to one for the first sensor, and where thesecond sensor's 32 effective searching time, T_(e2), 421 approachesinfinity (not shown, however, in the figure, but only a sharply risingcurve that ends at approximately 330s) in relation to the parallel line422, which marks a detection probability approaching zero for the secondsensor, and where the third sensor's 33 effective searching time,T_(e3), 431 approaches infinity (not shown, however, in the figure, butonly a sharply rising curve that ends at approximately 430s) in relationto the parallel line 432, which marks a detection probabilityapproaching zero for the third sensor. The detection probability is, asmentioned previously, a measurement of the probability of detecting atarget with a given target area and distance by a “single scan”, that isby one scan. FIG. 3 shows that the second target manoeuvre 342 iscarried out outside the circles 321, 331 for the ranges for the secondand third sensors 32, 33, respectively, and that the manoeuvre iscarried out within the circle 31 for the range for the first sensor.FIG. 4 also shows that for the second target manoeuvre 342 in FIG. 3 thesensor system's effective searching times, T_(ej), 441 are approximatelythe same as for the first sensor's 31 effective. searching times,T_(e1), 411, but it should be mentioned, however, that the sensorsystem's effective searching times, T_(ej), 441 are always strictly lessthan the effective searching times for the sensor that is locatedclosest in effective searching times.

[0130] At a second point in FIG. 4, for example at t=400, it can be seenthat the first sensor's 31 effective searching times, T_(e1), 411 andthe third sensor's 33 effective searching time, T_(e3), 431 increase andapproach infinity respectively, but that the second sensor's 32effective searching time, T_(e2), 421 approaches its minimum, which is aconsequence of the target's distance from the respective sensor. Thesecond sensor's 32 effective searching time, T_(e2), 421 has its minimumat a distance from the parallel line 422, which is a consequence of thetarget's distance from the second sensor 32.

[0131] The sensor system's effective searching time, T_(ej), 441 att=400 differs, however, from the second sensor's 32 effective searchingtime, T_(e2), 421, and is, in addition, lower. As the sensor system'seffective searching time, T_(ej), 441 at t=400 is lower than the secondsensor's 32 effective searching time, T_(e2), 421, the sensor system'sdetection probability, p_(ss,j), is higher than that of the closestsensor, which is the second sensor 32. Thus the sensor system has anequally good or better effective searching time than the individualsensors in the system, that is equally good or higher detectionprobability.

[0132] The knowledge that the sensor system has better performance thanthe individual sensors at certain points is important information for auser of the system. It can, for example, be used when planning where thesensors are to be set up in order to cover as large a surface aspossible with regard to the detection probability, or where the sensorsare to be set up in order to concentrate on meeting certainrequirements, for example by increasing the detection probability in aparticular geographical section by the use of the synergy effects thatarise when the sensor's ranges overlap each other.

[0133] Further analyses of a target path can be carried out on the basisof the analytical parameters calculated using the method according tothe invention, for example tracking accuracies can be calculated forindividual sensors and for the sensor system respectively, and trackingprobabilities for the target in question for individual sensors and forthe system respectively.

[0134] Further analyses can, of course, be carried out over an area ofthe sensor system, for example risks of target confusion in associationslots can be obtained with varying filter dimensioning. Associationslots relate to the volume that applies for a target. In addition, thetracking probabilities over the surface can be calculated analyticallyon the basis of the analytical parameters.

[0135] The invention is not to be regarded as being restricted by theembodiments and examples described, but can occur in additionalembodiments within the framework of the patent claims, for example theinvention can be used for sensors that are not of electromagneticnature. Examples of such sensors are sonars, which sensors are based onsound waves.

1. Method for an analysis tool for analysis of sensor performance for asystem of sensors, which method comprises analytical calculation of asensor system's measurement characteristics at each point in a givengeographical area, which method comprises: obtaining performanceparameters from N_(s) sensors that are in the system, characterized inthat: a set of analytical performance parameters for the system iscalculated by the performance parameters being fused irrespective of thedifferent measurement characteristics of the sensors in the system withregard to the given performance parameters and in that: the analyticalperformance parameters are used for analysis of the sensor system'sperformance.
 2. Method according to claim 1, characterized in thatobtaining performance parameters comprises obtaining performanceparameters comprising: p_(ss,i)=detection probability per scan fortargets with a particular target area for the sensor N_(s)=i;R_(i)=measurement accuracy expressed as covariance matrix for the sensorN_(s)=i; T_(i)=searching time for the search area for the sensorN_(s)=i, and: p_(fa,i)=the probability of false alarms for a sensor. 3.Method according to claim 2, characterized in that the calculation ofthe analytical performance parameters comprises calculations on thebasis of the performance parameters which calculations comprise theformulae: $\begin{matrix}{T_{j} = ( {\sum\limits_{i = 1}^{N_{S}}\quad T_{i}^{- 1}} )^{- 1}} & ( {7\text{-}2} ) \\{{\frac{1}{T_{e\quad j}} = {\sum\limits_{i = 1}^{N_{S}}\frac{p_{{s\quad s},i}}{T_{i}}}}\quad} & ( {7\text{-}3} ) \\{{{p_{{s\quad s},j} = \frac{T_{j}}{T_{e\quad j}}},}\quad} & ( {7\text{-}4} ) \\{{\frac{1}{T_{e\quad i}} = \frac{p_{{s\quad s},i}}{T_{i}}}\quad} & ( {7\text{-}5} ) \\{\quad {\mu_{i} = \frac{T_{e\quad j}}{T_{e\quad i}}}\quad} & ( {7\text{-}6} ) \\{\quad {R_{j} = \{ {\sum\limits_{i = 1}^{N_{S}}{\mu_{i}R_{i}^{- 1}}} \}^{- 1}}\quad} & ( {7\text{-}7} ) \\{\quad {p_{{f\quad a},j} = {\{ {\sum\limits_{i = 1}^{N_{s}}\frac{p_{{f\quad a},i}}{T_{i}}} \} T_{j}}}} & ( {7\text{-}8} )\end{matrix}$

where $T_{j},\frac{1}{T_{e\quad j}},$

p_(ss,j), μ_(i), R_(j) and p_(fa,j) comprise the analytical performanceparameters where N_(s) stands for the number of sensors in the systemand where the subscript j stands for “joint”, i.e. resulting.
 4. Methodaccording to claim 3, characterized in that probabilities for differentevents that concern the tracking procedure are calculated by using thecalculated measurement rate, $\frac{1}{T_{j}},$

the detection probability, p_(ss,j) and the probability of false alarms,p_(fa,j), for the sensor system together with Markov analysis.
 5. Methodaccording to claim 3, characterized in that a filter for the sensorsystem is calculated by using the calculated effective measurement rate,$\frac{1}{T_{ej}},$

for the system.
 6. Method according to claim 5, characterized in that:the said formulae are used to calculate the sensor system's measurementcharacteristics in order to calculate with a filter the sensor system'stracking performance for tracking measured objects, and in order thatthe filter for the system gives a covariant matrix, P, which is read offas a covariance matrix that gives the tracking accuracy of the sensorsystem at each point in a given area.
 7. Method according to claim 5,characterized in that the sensor system's stationary characteristics arecalculated by a filter's stationary state being calculated at each pointover a given area, which calculation comprises the said formulae: 8.Method according to claim 5, characterized in that the sensor system'sdynamic characteristics are calculated by a filter being calculatedbased on parallel target paths of a target with given values of speedand course, which calculation also comprises the said formulae: 9.Method according to claim 1, characterized in that an adaptive sensor isregarded as a sensor system.
 10. Device for analytical calculation of asensor system's performance comprising N_(s) sensors, which devicecomprises means for combining performance parameters in the form ofmeasurement characteristics from the respective said sensorscharacterized in that the device comprises means for fusion of theperformance parameters by weighting of the measurement contributions ofthe respective said sensors, which device comprises means forcalculating analytical performance parameters for the sensor system,which means for calculating analytical performance parameters for thesensor system is independent of the different measurementcharacteristics of the sensors in the system on account of the weightingof the measurement contribution of the respective said sensors. 11.Device according to claim 10, characterized in that the device comprisesmeans for calculating a filter's stationary state at each point over agiven area.
 12. Device according to claim 10, characterized in that thedevice comprises means for calculating a filter's dynamiccharacteristics on the basis of parallel target paths for a target withgiven values for speed and course.
 13. Device according to claim 10,characterized in that at least one of the sensors in the sensor systemis a passive sensor.
 14. Device according to claim 10, characterized inthat at least one of the sensors in the sensor system is an activesensor.
 15. Device according to claim 10, characterized in that at leastone of the sensors in the sensor system is an adaptive sensor. 16.Device according to claim 10, characterized in that at least one of thesensors in the sensor system is a radar unit.
 17. Use of a methodaccording to claim 1 and a device for a sensor system comprising atleast one sensor.